United were forced to settle for a fourth consecutive draw after a disappointing match at Selhurst yielded a share of the spoils.
In that run of draws, the last three have ended 0-0 and Reds manager Louis van Gaal later admitted he is concerned by the drought in front of goal that has now stretched to over five hours.
A draw was probably a fair result as neither side did enough to win, but United had to weather an early storm as Palace started brightly.
David de Gea saved well from Dwight Gayle before the Spanish goalkeeper was called into action again on seven minutes when he tipped Yannick Bolasie's well-struck effort onto the bar.
From the resultant corner, De Gea denied Scott Dann but, having survived that early pressure, United grew into the game and fashioned chances at the other end.
Wayne Rooney's inch-perfect diagonal ball picked out Ander Herrera, but no-one was there to meet the playmaker's volleyed cross.
The skipper had a free-kick well saved by Wayne Hennessey and then agonisingly failed to reach Anthony Martial's defence-splitting through ball.
Herrera fired wide from Martial's cut-back, but Palace remained a threat and should have gone ahead through Yohan Cabaye, who volleyed wide when well-placed on the hour mark.
While Herrera's claims for a penalty were waved away during a rare opening for the Reds, the Eagles continued to press for a goal and were almost rewarded on 76 minutes as Dann nodded just wide before, moments later, De Gea saved with his legs to keep out Gayle.
A speculative effort from Rooney sailed over the bar as United pushed for a late winner, but it was Palace who almost took all three points as Bolasie's header zipper over the crossbar.
Martial did have a goalbound shot inadvertently charged down by substitute team-mate Jesse Lingard, but United could have little complaint about the result.
Overall team performance: 6/10
United Faithful Man of the Match: Ander Herrera